Link to actual problem [9969] \[ \boxed {y^{\prime \prime }-a \left (y^{\prime } x -y\right )^{v}=0} \]
type detected by program
{"unknown"}
type detected by Maple
[[_2nd_order, _with_linear_symmetries]]
Maple symgen result This shows Maple’s found \(\xi ,\eta \) and the corresponding canonical coordinates \(R,S\)\begin{align*} \\ \left [R &= x, S \left (R \right ) &= \frac {y}{x}\right ] \\ \end{align*}
\begin{align*} \left [\underline {\hspace {1.25 ex}}\xi &= -\frac {x \left (v -1\right )}{2}, \underline {\hspace {1.25 ex}}\eta &= y\right ] \\ \left [R &= y x^{\frac {2}{v -1}}, S \left (R \right ) &= -\frac {2 \ln \left (x \right )}{v -1}\right ] \\ \end{align*}